Abstract
The deformation in nonrigid structure from motion can be modeled either in shape domain or in time domain. Here, we view the deformation in time domain, model the trajectory of each 3D point as a linear combination of trajectory bases, and present a novel method to automatically find the trajectory bases based on orthographic camera assumption. In this paper, a linear relation is explicitly derived between 2D projected trajectory and 3D trajectory bases. With this formulation, an approximation is formulated for finding 3D trajectory bases which cast the trajectory bases finding into a problem of finding eigenvectors. Using the approximated trajectory bases as a start point, an EM-like algorithm is proposed which refine the trajectory bases and the corresponding coefficients. The proposed method demonstrates satisfactory results on both the synthetic and real data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akhter, I., Sheikh, Y.A., Khan, S., Kanade, T.: Nonrigid structure from motion in trajectory space. In: Neural Information Processing Systems 2008 (December 2008)
Brand, W.: Morphable 3d models from video. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2001, pp. II–456–II–463, vol. 2 (2001)
Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3d shape from image streams, pp. 690–696 (2000)
Bue, A.D., Smeraldi, F., de Agapito, L.: Non-rigid structure from motion using ranklet-based tracking and non-linear optimization. Image Vision Comput. 25(3), 297–310 (2007)
Kanatani, K., Sugaya, Y.: Factorization without factorization: a complete recipe. Mem. Fac. Eng. Okayama Univ. 38, 61–72 (2004)
Olsen, S.I., Bartoli, A.: Implicit non-rigid structure-from-motion with priors. Journal of Mathematical Imaging and Vision 31(2), 233–244 (2008)
Poelman, C.J., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell. 19(3), 206–218 (1997)
Rabaud, V., Belongie, S.: Re-thinking non-rigid structure from motion. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1–8 (23-28, 2008)
Rosin, P.L., Marshall, A.D. (eds.): PNon-rigid 3D factorization for projective reconstruction. British Machine Vision Association (2005)
Tomasi, C., Kanade, T.: Shape and motion from image streams under orthography: a factorization method. International Journal of Computer Vision 9(2), 137–154 (1992)
Torresani, L., Hertzmann, A., Bregler, C.: Learning non-rigid 3d shape from 2d motion. In: Thrun, S., Saul, L., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems, vol. 16. MIT Press, Cambridge (2004)
Torresani, L., Hertzmann, A., Bregler, C.: Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors. IEEE Trans. Pattern Anal. Mach. Intell. 30(5), 878–892 (2008)
Triggs, B.: Factorization methods for projective structure and motion. In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 1996, pp. 845–851 (18-20, 1996)
Vogler, C., Li, Z., Kanaujia, A., Goldenstein, S., Metaxas, D.: The best of both worlds: Combining 3d deformable models with active shape models. In: IEEE 11th International Conference on Computer Vision, ICCV 2007, pp. 1–7 ( 14-21, 2007)
Wang, G., Wu, Q.M.J.: Stratification approach for 3-d euclidean reconstruction of nonrigid objects from uncalibrated image sequences. IEEE Transactions on Systems, Man, and Cybernetics, Part B 38(1), 90–101 (2008)
Xiao, J., Chai, J., Kanade, T.: A closed-form solution to non-rigid shape and motion recovery. International Journal of Computer Vision 67(2), 233–246 (2006)
Xiao, J., Kanade, T.: Uncalibrated perspective reconstruction of deformable structures. In: Tenth IEEE International Conference on Computer Vision, ICCV 2005, vol. 2, pp. 1075–1082 (17-21, 2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Su, Y., Liu, Y., Yang, Y. (2010). Optimal Trajectory Space Finding for Nonrigid Structure from Motion. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2010. Lecture Notes in Computer Science, vol 6474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17688-3_34
Download citation
DOI: https://doi.org/10.1007/978-3-642-17688-3_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17687-6
Online ISBN: 978-3-642-17688-3
eBook Packages: Computer ScienceComputer Science (R0)